An invariance principle for the edge of the branching exclusion process
type: Item
instance of: scholarly article
title: An invariance principle for the edge of the branching exclusion process
zbMATH Open document ID: 0732.60113
DOI: 10.1016/0304-4149(91)90069-O
author: N. E. Zubov
published in: Stochastic Processes and their Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors study a branching exclusion process with state space \(\{0,1\}^ Z\). Particles sitting in the lattice perform nearest neighbour symmetric random walks at rate \(\gamma\) with exclusion interaction - i.e. when a particle attempts to jump over an unoccupied site, the jump is suppressed - and each particle creates at rate \({1\over 2}\) a new particle at each unoccupied nearest neighbour site (in particular, particles which have been created will not disappear). It is shown that, for fixed \(\gamma >0\) and for any initial configuration \(\eta\) such that \(\eta\) (0)\(\neq 0\) and \(\sum_{x>0}\eta (x)<\infty\), under appropriate scaling, the position of the rightmost particle converges to a non-degenerate Brownian motion. The authors also obtain a shape theorem for the process starting with one occupied site.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4211244
zbMATH Keywords: branching exclusion process
zbMATH Keywords: nearest neighbour symmetric random walks
reviewed by: Klaus Schürger
MaRDI profile type: Publication
cites work: Front propagation in certain one-dimensional exclusion models.
cites work: Microscopic selection principle for a diffusion-reaction equation
cites work: Q5560061
cites work: Reaction-diffusion equations for interacting particle systems
cites work: Q5538132
cites work: Edge fluctuations for the one dimensional supercritical contact process
cites work: Q5768532
cites work: The central limit theorem for the right edge of supercritical oriented percolation
cites work: Q5185817
cites work: Q4170136
description: scientific article; zbMATH DE number 4211244